CHICAGO — Derrick Rose and Jimmy Butler have tried to stake a claim as the NBA’s best backcourt this season.

Against the Nets Tuesday night, however, they both looked lost.

Rose finished the game a dismal 2-for-15 and scored four points, while Butler — arguably the most improved player in the league this season — wasn’t much better, going 3-for-12 and scoring eight points as the Nets cruised to a 96-82 victory over the Bulls.

“We were just aggressive and got after them,” Nets coach Lionel Hollins said, “and they missed a bunch of shots.”

Though Deron Williams didn’t shoot the ball well (1-for-8, six points) he terrorized the Bulls defensively, and particularly during the second quarter when the Nets outscored Chicago 31-14 and turned the game around for good as Rose went 0-for-6 and committed two turnovers.

“Looking at the film last game, he got going by attacking, and so I wanted to make things a little more difficult and keep him guessing and put a little more pressure on him,” Williams said of his defense against Rose.

Butler didn’t do much better, pleasing his Nets counterpart, Joe Johnson. The two have had issues going back to the 2012-13 season, which ended for the Nets in a seven-game loss to the Bulls in the first round of the playoffs.

While Butler finished with eight points on 3-for-12 shooting, Johnson had 20 points and 11 rebounds — his first points-rebounds double-double in six years — and even though he said it didn’t mean anything more than usual afterward to play like this against Butler, the pause and smile that crept across his face gave away his true feelings on the subject.

“It’s just going out night in and night out and just competing,” Johnson said. “It’s not who I am playing against or trying to get up for. Obviously we’re trying to find ourselves as a team, and we’re just trying to improve and get better and that’s what we’re trying to do.”

Kevin Garnett being kept out of the lineup for rest didn’t come as a shock, because he had played three games in the previous four days and already had sat out the second half of four of the first six back-to-back sets this season.

The future Hall of Famer had missed four in a row after playing in both halves of the first back-to-back this season — Nov. 12 at Phoenix and Nov. 13 at Golden State — before playing Friday in Boston and Saturday at home against Indiana.